Best plan is to adjust the rear sight, to get it to shoot where you want it to shoot. Sighted about thirty to fifty yards is about right for iron sights. If it has the usual litle notched elevator, one notch may be too low, while the next one may be too high. If that is the case just file down a bit, the one that was too high.
If it is out sideways, tap the sight in its slot, in the direction you want the bullets to go.
Scopes designed for 22 rimfire rifles will fit the mount. Canadian tire have scopes suitable for it for about 30 dollars.
A really excellent rimfire scope is the Scorpion, designed and sold out of Winnipeg. The 4x, which I prefer over their variable, is about $60. I have one mounted on a Winchester 69A rifle and it is a very clear, solid scope.
Google Scorpion scopes.
I notice your rifle has "Mossberg" on it, indicating it was made by Mossberg. For many years, including up to about the mid 60s, Mossberg pretty well dominated the lower priced 22 sporting rifle class in in competetive shooting in north america. There were many different grades of Mossberg out there, but even the lowest priced ones were strong, reliable rifles and fairly accurate. The best Mossbergs had much better aperature sights and better triggers and came close to the Winchester 69A in quality.
I would place yours as one of the lower priced Mossberg's.